This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm3.2

Description: Join antecedents with conjunction ("conjunction introduction"). Theorem *3.2 of WhiteheadRussell p. 111. Its associated inference is pm3.2i and its associated deduction is jca (and the double deduction is jcad ). See pm3.2im for a version using only implication and negation. (Contributed by NM, 5-Jan-1993) (Proof shortened by Wolf Lammen, 12-Nov-2012)

		Ref	Expression
	Assertion	pm3.2	⊢ ( 𝜑 → ( 𝜓 → ( 𝜑 ∧ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜑 ∧ 𝜓 ) )
2	1	ex	⊢ ( 𝜑 → ( 𝜓 → ( 𝜑 ∧ 𝜓 ) ) )